"专事诽谤的人" can be translated into English as "a dedicated slanderer" or "a professional defamer".
"A dedicated slanderer" emphasizes that the person is wholly committed to spreading false and damaging statements about others.
"A professional defamer" suggests that the person engages in slandering as a regular or even paid activity.
Both expressions convey the idea of someone who habitually or intentionally engages in slander.